Question: Simplify. Rewrite the expression in the form $x^n$. $\left(x^2\right)^{4}=$
Answer: $\begin{aligned} \left(x^2\right)^{4}&=x^{2\cdot 4} \\\\ &=x^{8} \end{aligned}$ This follows from the general rule $\left(x^m\right)^{n}=x^{m\cdot n}$. We can also see this is correct by expanding the powers. $\begin{aligned} \left(x^2\right)^{4}&=\underbrace{x^2\cdot x^2\cdot x^2\cdot x^2}_\text{4 times} \\\\\\ &=\underbrace{ \underbrace{x\cdot x}_\text{2 times} \cdot \underbrace{x\cdot x}_\text{2 times} \cdot \underbrace{x\cdot x}_\text{2 times} \cdot \underbrace{x\cdot x}_\text{2 times}} _\text{4 times} \\\\ &=x^{8} \end{aligned}$ In conclusion, $\left(x^2\right)^{4}=x^{8}$.